Global dynamics of a tuberculosis model with sensitivity of the smear microscopy

Das, Dhiraj Kumar; Kar, Tapan Kumar

doi:10.1016/j.chaos.2021.110879

Cited by 25 publications

(6 citation statements)

References 36 publications

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“…Therefore, it is necessary to study the influence of various parameters on the basic reproduction number to make a control policy. A model's most sensitive parameters are calculated using the sensitivity index approach [16,38,39]. The data collection process and presumed parameter values are usually error-prone.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach

Majee¹,

Jana²,

Barman³

et al. 2023

Phys. Scr.

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Presently, monkeypox virus infection has spread worldwide in the ongoing outbreak that began in the UK. To study the transmission dynamics of monkeypox, we formulate here a seven-compartmental (five compartments for the human population and two compartments for animals or rodents) fractional-order mathematical model. The existence and uniqueness of the solution of the proposed fractional order model are examined here. The basic reproduction number for humans ($\mathfrak{R}_0^h$) and animals ($\mathfrak{R}_0^a$) are obtained through the next-generation matrix approach. Depending on the values of $\mathfrak{R}_0^h$ and $\mathfrak{R}_0^a$, we observed that the fractional order model has three equilibria, namely, monkeypox-free equilibrium, animal-free endemic equilibrium, and endemic equilibrium. Also, the stability of all equilibria is checked in this present article. We found that the model goes through transcritical bifurcation at $\mathfrak{R}_0^a=1$ for any values of $\mathfrak{R}_0^h$ and at $\mathfrak{R}_0^h=1$ for $\mathfrak{R}_0^a<1$. Best of our knowledge, this is the first work where the fractional order optimal control for monkeypox is formulated and solved considering vaccination and treatment controls. Several feasible parameter values are used in the simulations to visualize and verify the findings, from which the results show that fractional order is more appropriate. Finally, parameters involved in the expression of $\mathfrak{R}_0^h$ and $\mathfrak{R}_0^a$ are scaled using the sensitivity index approach.

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Section: Sensitivity Analysismentioning

confidence: 99%

Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach

Majee¹,

Jana²,

Barman³

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…It is very essential to discuss the sensitivity of model parameters to study the dynamics of the system. For example, the sensitivity index of the basic reproduction number R 0 to parameter Λ can be defined as [55] Γ…”

Section: Sensitivity Analysismentioning

confidence: 99%

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Sun

Zhao

2023

Fractal Fract

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The fractional differential equation has a memory property and is suitable for biomathematical modeling. In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Firstly, for the deterministic fractional system, the threshold conditions for the local and global asymptotic stability of the equilibrium point are obtained by using the stability theory of the fractional differential equation. If R0<1, the disease-free equilibrium is asymptotically stable, and the disease is extinct; when R0>1, the endemic equilibrium is asymptotically stable and the disease persists. Secondly, for the stochastic system of integer order, the stochastic stability near the positive equilibrium point is discussed. The results show that if the intensity of environmental noise is small enough, the system is stochastic stable, and the disease will persist. Thirdly, the control variables are coupled into the fractional differential equation to obtain the fractional control system, the objective function is constructed, and the optimal control solution is obtained by using the maximum principle. Finally, the correctness of the theoretical derivation is verified by numerical simulation.

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“…To determine that the model ( 1 ) possesses a unique solution, we follow the methodology given in 32 and define the vector field of the proposed model as where The right-hand side of the Eq. ( 3 ) implies that the function H is continuous and therefore ensures the existence of solution ( S , A , B , R ) over an interval .…”

Section: Problem Formulationmentioning

confidence: 99%

Modelling the dynamics of acute and chronic hepatitis B with optimal control

Khan,

Rihan,

Ahmad

2023

Sci Rep

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This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin’s Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis.

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Global dynamics of a tuberculosis model with sensitivity of the smear microscopy

Cited by 25 publications

References 36 publications

Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach

Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Modelling the dynamics of acute and chronic hepatitis B with optimal control

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